Defeat to their city rivals leaves los Blancos nine points behind league leaders Barcelona and their coach, frustrated at their display, feels the prize is now a bridge too far.
Real Madrid cannot win La Liga after Saturday's 1-0 defeat to rivals Atletico Madrid, according to coach Zinedine Zidane.
Antoine Griezmann's second-half goal secured a narrow 1-0 victory against the hosts to wrap up their third consecutive victory against their rivals at the Santiago Bernabeu.
Defeat leaves Zidane's side nine points behind league leaders Barcelona, who are yet to play Sevilla on Sunday evening and could go 12 points clear at the top with a win.
And the 43-year-old concedes they are now too far behind to stand a chance of catching the Catalans, but still states his men will not put any less effort in.
"Before you ask, the league is over," the Frenchman told reporters in his press conference. "It was always difficult. I told the players yesterday that if we lose points it will be more difficult.
"We are not going to throw the league away though, whatever happens."
Atletico played out a 0-0 draw with PSV in the Champions League on Wednesday while Madrid had not played since a 1-1 draw with Malaga in La Liga on Sunday.
The fact los Blancos had the entire week to prepare for the derby left Zidane underwhelmed by the result, claiming his side did not exploit any potential fatigue in their opponents.
"I'm not happy with the match and I'm not happy with the result," he continued. "The important thing for me and the team is to think about the next game.
"We didn't play the game how we prepared, so it's here we had to work more.
"When you play against a team who played on Wednesday you need to do more. They can't go into the match and be comfortable and that's what they did so it's more difficult to take."